Variation / Proportional

Direct Variation / Directly Proportional

y is directly proportional to x, y ∝ x:
 
$y = kx$

k = constant of proportionality
y varies directly as x is another statement equivalent to the above statement.

 

Inverse Variation / Directly Proportional

y is inversely proportional to x, y ∝ 1/x:
 
$y = \dfrac{k}{x}$

k = constant of proportionality
y varies inversely with x holds the same meaning as the sentence above.

 

Joint Variation / Jointly Proportional

y is directly proportional to x and z:
$y = kxz$

 

y is directly proportional to x and inversely proportional to z:

$y = \dfrac{kx}{z}$

 

k = constant of proportionality

 

Variation to nth power of x and mth power of z

y is directly proportional to the square of x and varies inversely to the cube of z:
 
$y = \dfrac{kx^2}{z^3}$

k = constant of proportionality

 

Tags
direct variation
inverse variation
joint variation
directly proportional
inversely proportional
jointly proportional
constant of proportionality